Answer:
[tex]\boxed {\boxed {\sf (5, -3)}}[/tex]
Step-by-step explanation:
We are asked to solve the system of equations by substitution. We must isolate a variable and plug it into the other equation.
We are given these 2 equations;
[tex]2x-3y=19[/tex]
[tex]x-2y=11[/tex]
1. Isolate a Variable
We can easily isolate x in the 2nd equation. 2y is being subtracted from x. The inverse operation of subtraction is addition. Add 2y to both sides of the equation.
[tex]x-2y+2y=11 +2y \\x= 11+2y[/tex]
2. Substitute and Solve for y
x is equal to 11 + 2y, so we can substitute this expression in for x in the 1st equation.
[tex]2x-3y=19[/tex]
[tex]2(11+2y)-3y=19[/tex]
Now we can solve for y by isolating the variable First, distribute the 2. Multiply each term in parentheses by 2.
[tex](2*11) + (2*2y) -3y = 19[/tex]
[tex]22 + 4y-3y = 19[/tex]
Combine the like terms.
[tex]22+y=19[/tex]
22 is being added to y. The inverse operation of addition is subtraction. Subtract 22 from both sides of the equation.
[tex]22-22+y=19-22\\y= 19-22 \\y= -3[/tex]
3. Solve for x
We know that y is equal to -3, so we can plug it back into either original equation and solve for x. Let's use the 2nd equation.
[tex]x-2y=11[/tex]
[tex]x-2(-3)=11[/tex]
Multiply -2 and -3.
[tex]x+6=11[/tex]
6 is being added to x. The inverse operation of addition is subtraction. Subtract 6 from both sides of the equation.
[tex]x+6-6=11-6\\x=11-6 \\x=5[/tex]
We found that y=-3 and x=5. Coordinate points are written as (x,y), so the solution for this system of equations is (5, -3).
